Description

Functions for calculating coordinate representations of hypocycloids,
epicyloids, hypotrochoids, and epitrochoids (altogether called
'cycloids' here) with different scaling and positioning options.
The cycloids can be visualised with any appropriate graphics
function in R.

Details

Package:

cycloids

Type:

Package

Version:

1.0

Date:

2013-10-24

License:

GPL-3

This package has been written for calculating cartesian coordinate
representations of hypocycloids, epicyloids, hypotrochoids, and
epitrochoids (altogether called 'cycloids' here). These can be
easily visualized with any R graphic routine that
handles two-dimensional data. All examples shown here use
standard R graphics. While there are technical applications, the
main purpose of this package is to create mathematical artwork.
Geometrically, cycloids in the sense of this package are generated as
follows (Figure 1, 2): Imagine a circle cfix, with radius
A, which is fixed on a plane. Another circle, cmov,
with radius a, is rolling along cfix's circumference
at the outside of cfix. The figure created by the trace of
a point on cmov's circumference is called an epicycloid (Figure 1A).
If cmov is rolling not at the outside but at the inside of
cfix, the trace of a point on cmov's circumference
is called a hypocycloid (Figure 2A).
If in both cases the tracepoint is not located on
cmov's circumference but at a fixed distance from its midpoint
either in- or outside cmov, the resulting figure is an epitrochoid (Figure 1B, C)
or a hypotrochoid (Figure 2B, C), respectively. Hypotrochoids and epitrochoids
became quite popular through toys like the spirograph.
The most important functions of the package are
zykloid, zykloid.scaleA,
zykloid.scaleAa, and zykloid.scaleP.